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Problem Title: The Leaves of a Tree

  Year: 2012      
  Student Level: Undergraduate      
  Source: MCM      
  Commentary: Yes (1)      
  Student Papers: Yes (5)      

"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:

  • Why do leaves have the various shapes that they have?
  • Do the shapes "minimize" overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the "volume" of the tree and its branches effect the shape?
  • Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?
  • How would you estimate the leaf mass of a tree?

Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)? In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.


Judges' Commentary: The Outstanding Leaf Problem Papers

Peter Olsen, P.E.
Commander, US Coast Guard Reserve

  Student Papers      

Team 14297: The Leaves of a Tree

Hong Kong Baptist University, China


Team 14990: A Close Look On Leaves

Shanghai Foreign Language School, China


Team 15065: Geometrical Tree Leaf mass & leaf-tree relationship

National University of Singapore, Singapore


Team 16831: The Secrets of Leaves

Zhejiang University, China


Team 17164: Probabilistic Models to Predict the Mass and Shapes of Leaves in a Tree

Cornell University, NY